Labour's candidate for London Mayor had claimed during a radio debate that Mr Johnson had, like him, set up a company so he could avoid paying tax on his media earnings.

Mr Johnson was reportedly left 'red-faced' and 'utterly furious' by the allegations, and after the debate he squared up 'nose to nose' with his rival and repeatedly called him a 'f****** liar'.

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Clash: Ken Livingstone accused Boris Johnson of using the same tax 'arrangements' that he came under fire for during an hour long radio debate at LBC studios in central London

War of words: An outraged Boris Johnson branded Ken Livingstone a 'liar' while discussing their taxes during the live radio session

Later in the day, the London Mayor released a letter from his accountants to prove Mr Livingstone's allegations were untrue.

The clash occurred as the two men were travelling in a lift up to the roof terrace at the LBC radio station to be photographed after taking part in a live mayoral debate ahead of next month's elections.

Liberal Democrat Brian Paddick and Green candidate Jenny Jones were also in the lift.

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Mr Johnson was 'visibly shaking with anger' and was 'right up in Mr Livingstone's face' when he began swearing, sources claimed.

The outburst came after Mr Livingstone accused the mayor of having 'the same arrangements' for dealing with his media earnings as him.

Labour's candidate has come under attack for 'tax dodging' in recent weeks over claims that he was paid via a private company called Silveta Ltd so he was liable for only corporation tax at 20 per cent instead of income tax.

Head-to-head: Current London mayor Boris Johnson, left, and Labour's Ken Livingstone, right, arriving at LBC radio studios in London for a live debate that descended into a furious clash between the two politicians

It is understood the mayor talked to his opponent privately after a business hustings three weeks ago to tell him what he had been saying about his tax arrangements was not true and he was furious when Mr Livingstone then repeated the claims on the airwaves.

On the radio show, Mr Johnson called the accusation 'lies', adding: 'I have never used a company to minimise my tax.' He later issued a statement rebutting the allegations, adding: 'The real point is not about my tax arrangements.

'It is about the hypocrisy of a man who for years has railed against those who use special arrangements to reduce their tax and who has then been caught – bang to rights – doing the very same thing himself.'

Mr Johnson also released letters from his accountant Robert Maples, who wrote: 'My firm has acted as Boris's accountants since the 1990s. All of his freelance earnings have been included in his tax returns and subjected to income tax at the appropriate rates.'

A spokesman for Mr Livingstone said he stood by his claims, adding: 'Boris Johnson lost his temper because he lost the debate.'

Mr Livingstone's attack comes just weeks after it emerged he had used a loophole to avoid £50,000 in tax. He was accused of hypocrisy because he had previously attacked tax avoiders as 'rich b******s'.

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F-words, 'lies' and the day election rivals Boris and Ken went nose to nose in a lift